`BookProof.SmDiracSpinor.diracFieldHam_symmetric` (psi phi : FermiFock 4) : (inner ℂ (diracFieldHam k m1 m2 psi) phi : ℂ) = inner ℂ psi (diracFieldHam k m1 m2 phi)

Proved

BookProof.SmDiracSpinor.diracFieldHam_symmetric

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracSpinor.

BookProof.SmDiracSpinor.diracFieldHam_symmetric (psi phi : FermiFock 4) : (inner ℂ (diracFieldHam k m1 m2 psi) phi : ℂ) = inner ℂ psi (diracFieldHam k m1 m2 phi)

Formalization note: Lean 4 identifier BookProof.SmDiracSpinor.diracFieldHam_symmetric.

Preamble

-- Generated from ChapterSmDiracSpinor.lean — theorem BookProof.SmDiracSpinor.diracFieldHam_symmetric
import Definitions.Def_ChapterCPTHamiltonian
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracSpinor
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar
open BookProof.SmDiracSpinor



open Matrix
open BookProof.ChapterCPTHamiltonian BookProof.SmCar BookProof.SmDiracYukawa
open BookProof.FarisLavine

noncomputable section

variable {k : Fin 3 → ℝ} {m1 m2 : ℝ}

Formal statement

theorem BookProof.SmDiracSpinor.diracFieldHam_symmetric (psi phi : FermiFock 4) :
    (inner ℂ (diracFieldHam k m1 m2 psi) phi : ℂ)
      = inner ℂ psi (diracFieldHam k m1 m2 phi) := by sorry

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